Process for Fabry-Perot filter train configuration using derived mode field size

ABSTRACT

A process for configuring a tunable MOEMS filter train comprises determining a spectral response of a MOEMS tunable filter. A spectral separation between different order modes, or free spectral range, is then determined for the filter. This information is then related to a mode size of a desired mode of the tunable filter. With this information, lenses for the optical train are provisioned, and then installed so that light is launched into the optical filter at the desired mode size to thereby maximize the SMSR of the filter train.

This application is a continuation of U.S. application Ser. No.09/809,667 filed Mar. 15, 2001 now U.S. Pat. No. 6,377,386.

BACKGROUND OF THE INVENTION

Tunable optical filters are useful in situations requiring spectralanalysis of an optical signal. They can also be used, however, asintra-cavity laser tuning elements or in tunable detectors, for example.One of the most common, modem applications for these devices is inwavelength division multiplexing (WDM) systems. WDM systems transmitmultiple spectrally separated channels through a common optical fiber.This yields concomitant increases the data throughput that can beobtained from a single optical fiber. There are additional advantagesassociated with the ability to use a single fiber amplifier to amplifyall of the channels on an optical link and its use as a platform fordynamic channel/wavelength routing.

Tunable filters that operate in these WDM systems must typically be highquality/high finesse devices. Currently proposed standards suggestchannel spacings of 100 GigaHertz (GHz) to channel spacings as tight as50 GHz in the ITU grid; some systems in development have spacing of 20GHz and less. Tunable filter systems that operate in systems having suchtight channel spacings must have correspondingly small passbands whenoperating as monitors, receivers, and routing devices.

Typically, the design of the tunable filters is based on a class ofdevices generally referred to as Fabry-Perot (FP) etalons. These deviceshave at least two highly reflective elements defining the Fabry-Perotcavity. The tunability functionality is provided by modulating theoptical length of the cavity.

Since these tunable filters are typically incorporated into largersystems offering higher levels of functionality and because theFabry-Perot cavity must be modulated over distances corresponding to thewavelength of light that it is filtering, typically around 1,000 to2,000 nanometers (nm) in wavelength, microoptical electromechanicalsystems (MOEMS) technology is typically used to fabricate the tunablefilters. The most common implementation pairs anelectrostatically-deflectable reflective optical membrane with a fixedreflector. Thin film technology is typically used to obtain thereflectivity. High finesse systems can require dielectric mirrors havinggreater than seven layers.

A common metric for characterizing the quality of tunable filter systemsis the side mode suppression ratio (SMSR). This is the ratio between themagnitude of the lowest order mode in the spectral plot of the filter'scharacteristic and the magnitude of the next largest mode, which istypically the next higher order mode.

A general configuration for MOEMS tunable filter Fabry-Perot cavities istermed a curved-flat cavity. In such cavities, one of the reflectors isnear planar and the other reflector is curved. If the curved reflectorhas a spherical profile, the cavity is sometimes referred to as ahemispherical cavity.

When hemispheric tunable filters are used, for example, the opticaltrain surrounding the filter must be designed with the objective tocontrol SMSR.

One solution to controlling SMSR used in some conventional MOEMS filtersystems is to integrate the tunable filter into the larger opticalsystem by locating it between two fiber pigtails; one fiber pigtailemits the optical signal to be filtered and the other fiber pigtailcollects the filtered optical signal after its transmission through thetunable filter. The tunable filter is oriented to be orthogonal to theaxis extending between the fiber endfaces.

SUMMARY OF THE INVENTION

As optical systems are developed that allow for higher levels offunctionality in a single package, increased attention is directed tothe co-design of the tunable filter element and surrounding opticalsystem. This is especially true in systems utilizingfree-space-interconnects between the tunable filter and other opticalcomponents in the system.

One parameter that affects the SMSR of a MOEMS filter system is modesize matching between the lowest order transverse mode of the tunablefilter and the mode size of the light as it is launched into the tunablefilter. The mode field diameter is a measure of the radial intensitydistribution of radiation. Mode field diameter is measured by the ITU-Treference test method based on the far field scan technique. Theintensity of the radiation reaching the photodiode is recorded as afunction of angle; and from these data, the mode field diameter iscalculated. According to one definition, weighted mean of the angularradial intensity distribution is used. If the mode size of the lightthat is launched into the filter is smaller or larger than the lowestorder mode of the filter, higher order modes will be excited, therebydegrading the performance of the system.

The spectral output of a Fabry-Perot filter, in general, comprisesmultiple spectrally distributed peaks in the filter's response to abroadband light source. These different peaks are attributable to thelongitudinal mode orders of operation of the cavity and the cavity'stransverse spatial modes. The pattern of the peaks repeats itselfspectrally with a periodicity that is related to the separation betweenthe mirrors, termed the free spectral range. Within a given order oflongitudinal mode operation, the frequency separation between transversemodes is related to the curvature of the mirrors. Specifically, forHermite-Gaussian transverse modes the spectral separation between thelowest-order mode and any higher-order mode with mode number (n,m) aregiven by: $\begin{matrix}{{\Delta \quad v_{HOM}} = \quad {( {n + m + 1} ){\arccos \lbrack {{{sqrt}( {1 - \frac{L}{r_{1}}} )} \cdot {{sqrt}( {1 - \frac{L}{r_{2}}} )}} \rbrack}{c/( {2\pi \quad L} )}}} \\{= \quad {( {n + m + 1} ){{\arccos \lbrack {{sqrt}( {g_{1} + g_{2}} )} \rbrack} \cdot \frac{c}{2\pi \quad L}}\quad {where}\quad g_{1}}} \\{{= \quad {{1 - {{L/r_{1}}\quad {and}\quad g_{2}}} = {1 - {L/r_{2}}}}},{{where}\quad {r1}}}\end{matrix}$

and r1 are the radii of curvature of the two mirrors and L is the mirrorseparation.

Typically, one of the mirrors will have a known radius of curvature, forexample, in a curved-flat cavity. Such information can be determinedusing white-light interferometery or other surface profilometry. Theother mirror's radius can thus be computed.

This scheme is useful in the situation where the known mirror has arelatively small radius, and thus can be measured accurately. When thesecond mirror has a very long radius, it is difficult to measure itsradius, especially if its effective aperture is small.

The present invention is directed to a technique for determining themode size of a MOEMS tunable Fabry-Perot filter by reference to acalculated value for the curvatures of the reflectors that form theFabry-Perot tunable filter cavity. Specifically, in the case of aconcentric Fabry-Perot cavity or related cavity where one of the mirrorsis relative flat, the curvature of the curved reflector is calculatedfrom the spectral response of the tunable filter.

In general, according to one aspect, the invention features a processfor configuring a tunable MOEMS filter train. The process comprisesdetermining a spectral response of a MOEMS tunable filter. A spectralseparation between different order longitudinal modes, or free spectralrange, is then determined for the filter, as well as transverse modespectral separation. This information is then related to a mode size ofa desired mode of the tunable filter. With this information, lenses forthe optical train are provisioned, and then installed so that light islaunched into the optical filter at the desired mode size to therebymaximize the SMSR of the filter train.

In specific embodiments, the mode size of the injected optical signal isdetermined for the filter train. In the case of light being launchedfrom a single mode optical fiber, the mode size is about 8-10micrometers in diameter.

In one implementation, the spectral response of the tunable filter canbe determined by tuning the tunable filter across a laser light sourceor other source that generates a spectrally narrow line. In anotherimplementation, the filter spectral response is determined by injectingbroadband “white” light into the filter and measuring the transmittedlight spectrum.

According to other aspects of the preferred embodiment, the step ofdetermining the spectral separation comprises determining a spectralseparation between a lowest order mode and a next higher order modewithin an order of operation of the tunable filter. Using thisinformation, lenses in the optical train are selected to have beamforming characteristics that will yield the desired mode size at thetunable filter. These provisioned lenses are then installed in thefilter train.

According to another implementation, the location of the lenses in thefilter train can be adjusted to achieve the desired mode size at thetunable filter.

The above and other features of the invention including various noveldetails of construction and combinations of parts, and other advantages,will now be more particularly described with reference to theaccompanying drawings and pointed out in the claims. It will beunderstood that the particular method and device embodying the inventionare shown by way of illustration and not as a limitation of theinvention. The principles and features of this invention may be employedin various and numerous embodiments without departing from the scope ofthe invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, reference characters refer to the sameparts throughout the different views. The drawings are not necessarilyto scale; emphasis has instead been placed upon illustrating theprinciples of the invention. Of the drawings:

FIG. 1 is a perspective view of an optical channel monitor to which thepresent invention is applicable, in one example;

FIG. 2 is a schematic block diagram showing a tunable filter trainaccording to the present invention;

FIG. 3 is a process diagram illustrating the inventive tunable filtertrain configuration process for mode field diameter matching; and

FIG. 4 is a spectral plot showing a lowest order mode and a next higherorder mode within an order of operation of the tunable filter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates the integration of the optical channel monitoringsystem on a single, miniature optical bench 2.

Specifically, the fiber 10 is terminated on the bench 2 at a mountingand alignment structure 252. This mounting and alignment structure 252holds the fiber in proximity to a first collimating lens 14, which isheld on its own mounting and alignment structure 254. The firstcollimating lens forms a signal beam that is transmitted through anoptional isolator 60.

After the isolator, a focusing lens 16 focuses the beam onto a tunableMOEMS filter 18, which is held on the filter mounting and alignmentstructure 259.

In one implementation, a reference signal optical train is furtherprovided. Specifically, a super luminescent light emitting diode (SLED)52 generates the broadband beam, which is focused by the secondcollimating lens 54 held on mounting and alignment structure 256. Thiscollimates the beam to pass through the etalon 56 installed on the bench2. A reference beam generated by the etalon is reflected by fold mirror58 to a first WDM filter 50 in the signal beam path. As a result, acombined beam is transmitted through the isolator 60 and the tunablefilter.

The filtered, combined beam from the filter 18 is re-collimated by athird collimating lens 62 held on mounting and alignment structure 260.This beam is then separated into the filtered reference beam and thefiltered signal beam by a second WDM filter 64. The reference signal isdetected by reference photodiode 66. The filtered optical signal istransmitted through the second WDM filter 64 to the signal photodiode68.

FIG. 2 is a schematic diagram of the portion of the filter train for thetunable that defines the launch criteria for the optical signal into thetunable filter and thus, the filter's and system's SMSR. Specifically,the fiber 10 is preferably single mode. It launches the optical signalin the form of a beam into the first lens 14. This generally improvesthe collimation of the beam or forms a beam waist between the first lens14 and the second lens 16. In the preferred embodiment, the focallengths of the first and second lenses are between 1.0 and 2.0millimeters. In a current implementation, the focal length of the firstlens 14 is about 1100 μm and of the second lens is about 1600 μm. Thespacing between the first lens and the fiber endface is less than 1.0millimeter, or presently about 500 μm. The spacing between the firstlens 14 and of second lens 16 is between 2 and 10 mm, presently it isabout 6 mm. Finally, the spacing between the second lens and thereflecting membrane 110 of the tunable filter 18 is between 0.5 and 3mm. Presently, it is about 1 mm. In the current implementation, themembrane 110 is silicon and the curved reflector 120 is silicon orgallium phosphide.

With these parameters, the nominal magnification of the tunable filtertrain, comprising lenses 14, 16, is two. Generally, the magnificationshould be between 1 and 5. Thus, the 10 micrometer diameter mode sizeemitted from the endface 12 of the fiber 10 is converted to a 20micrometer beam diameter at the tunable filter 18. Generally, the modefield diameter of the lowest order mode for the filter is between 10 and50 micrometers.

FIG. 3 shows the process for configuring the tunable filter trainaccording to the present invention. Specifically, the mode size of theinjected signal is determined in step 310. Specifically, this mode sizeis approximately 8-10 micrometers in the current embodiment, which isthe typical mode size in single mode fiber for wavelengths surrounding1,550 nm.

Also, in step 320, the spectral response of the MOEMS tunable filter isdetermined. In one implementation, a signal from a laser source or othernarrow-band signal is injected into the MOEMS tunable filter 18, whilethe tunable filter is scanned across the signal. Thus, the temporalresponse is roughly equivalent to the filter's spectral response.Exemplary spectral plot is illustrated in FIG. 4. Within the illustratedorder of operation, there is a lowest order mode 410, higher ordersatellite modes 412, 414 that are attributed to the transverse spatialmodes of the FP cavity.

Next, in step 330, the spectral separation between the filter modes isdetermined. Specifically, the nanometer separation between mode 410 andmode 412 in FIG. 4 is determined in the preferred embodiment, sincethese are typically the highest power modes in the signal. Additionally,in the preferred embodiment, the free spectral range of the filter isdetermined. This is the spectral separation between the different ordersof the filter operation, which correspond to the different longitudinalmodes of the filter cavity.

Next, the desired mode size is determined in step 340. Specifically, thefollowing set of calculations are used to determine that mode size inone embodiment in which, the mirror 120 is gallium phosphide (GaP), themembrane 110 is silicon, and the free spectral range is 76 nanometers.

Note: All Dimensions in Microns.

Based on the measured HOM spacing (the odd mode-fundamental), deduce theg1g2 product to calculate the radius of curvature of the Mems Membrane110. Then, determine the mode-matched spot sized launched from eitherthe Si or the GaP side.

R_(GaP):=−1055 Negative value of R is for concave mirror (as beam seesit)

λ:=1.559034 μm Fundamental wavelength

λ_(next):=1.635102 μm Next order wavelength

λ_(odd):=λ−0.003388 μm FSR (nm) $\begin{matrix}{{\Delta \quad v}:={\frac{c}{\lambda} - \frac{c}{\lambda_{next}}}} & {\quad {{\Delta \quad v} = {8.946 \times 10^{12}\quad {Hz}}}} & {\quad {{( {\lambda_{next} - \lambda} ) \cdot 1000} = {76.086\quad \mu \quad m}}}\end{matrix}$ $\begin{matrix}{\underset{\_}{L}:={\frac{c}{{2 \cdot \Delta}\quad v}}} & {\quad {\underset{\_}{L} = {16.756\quad \mu \quad m}}}\end{matrix}$ $\begin{matrix}{{\Delta \quad v_{HOM}}:={\frac{c}{\lambda_{odd}} - \frac{c}{\lambda}}} & {{\Delta \quad v_{HOM}} = {4.191 \times 10^{11}\quad {Hz}}}\end{matrix}$$g_{1}:=\frac{( {\cos ( {\Delta \quad {v_{HOM} \cdot 2 \cdot \underset{\_}{L}}\frac{\pi}{c}} )} )^{2}}{1 + \frac{\underset{\_}{L}}{R_{GaP}}}$$R_{mems}:=\frac{\underset{\_}{L}}{g_{1} - 1}$

R_(mems):=2949 μm (radius of curvature of silicon membrane 110)

Calculate beam diameters at mirrors for a spherical resonator, thendetermine the optical launch condition from either Si or GaP side

L:=16.756 μm

R_(mems):=−2948.9 μmλ:=1.559034 μm

R_(GaP):=−1055 μm $\begin{matrix}{z_{1}:=\frac{- {L( {R_{mems} + L} )}}{R_{mems} + R_{GaP} + {2 \cdot L}}} & {z_{1} = {- 12.374}} & \begin{matrix}{{{position}\quad {of}\quad {mirror}\quad 1}\quad} \\{{{wrt}\quad {beam}\quad {waist}\quad {at}\quad z} = 0}\end{matrix}\end{matrix}$ $\begin{matrix}{{\begin{matrix}{z_{2}:={z_{1} + L}} & {\quad z_{2}}\end{matrix} = 4.382}\quad} & \begin{matrix}{{{position}\quad {of}\quad {mirror}\quad 2}\quad} \\{{{wrt}\quad {beam}\quad {waist}\quad {at}\quad z} = 0}\end{matrix}\end{matrix}$$z_{0}:=\sqrt{\frac{{- L} \cdot ( {R_{GaP} + L} ) \cdot ( {R_{mems} + L} ) \cdot ( {R_{mems} + R_{GaP} + L} )}{( {R_{mems} + R_{GaP} + {2 \cdot L}} )^{2}}}$rayleigh  range, beam  radius  is  sqrt  (2)  larger  than  waist  here, 2z₀ = depth  of  focus$\begin{matrix}{w_{0}:=\sqrt{\lambda \cdot \frac{z_{0}}{\pi}}} & {\quad {w = {7.508\quad {waist}\quad {radius}}}}\end{matrix}$ $\begin{matrix}{w_{1}:={w_{0} \cdot \lbrack {1 + ( \frac{z_{1}}{z_{0}} )^{2}} \rbrack^{\frac{1}{2}}}} & {w_{1} = {7.552\quad {spot}\quad {radius}\quad {at}\quad {mirror}\quad 1}}\end{matrix}$ $\begin{matrix}{w_{2}:={w_{0} \cdot \lbrack {1 + ( \frac{z_{2}}{z_{0}} )^{2}} \rbrack^{\frac{1}{2}}}} & {w_{2} = {7.513\quad {spot}\quad {radius}\quad {at}\quad {mirror}\quad 2}}\end{matrix}$

Spot size at curved mirror=2·w₁=15.105 μm=spot diameter at {fraction(1/e)}² power Spot size at flat mirror=2·w₂=15.027 μm

Calculate the optimum launch condition for mode—matching to either side.

Calculate the required spot size in air since we can measure itdirectly.

Launching from the GaP Mirror

n:=3.052 L:=200

r_(c):=R_(GaP) W_(c):=W₁$q_{2} = \lbrack ( {\frac{1}{r_{c}} - \frac{i \cdot \frac{\lambda}{n}}{\pi \cdot w_{c}^{2}}} )^{- 1} \rbrack$

q₂=−105.021+315.86i $\begin{matrix}{q_{0{im}}:={{Im}( \frac{q_{2} - L}{n} )}} & {\quad {q_{0{re}}:={{Re}( \frac{q_{2} - L}{n} )}}} & {\quad {q_{0{im}} = 103.493}}\end{matrix}$

q₀:=q_(0re)+i·_(0im) q_(0re):=−99.941

The radius of curvature and spot entering the GaP Mirror are$\begin{matrix}{R_{i\quad n}:=\frac{1}{{Re}( \frac{1}{q_{0}} )}} & {\quad {R_{i\quad n} = {- 207.112}}}\end{matrix}$ $\begin{matrix}{w_{i\quad n}:=\sqrt{\frac{- \lambda}{\pi} \cdot \frac{1}{{Im}( \frac{1}{q_{0}} )}}} & {{2w_{i\quad n}} = 19.925}\end{matrix}$

Therefore, the spot size at the waist in air is $\begin{matrix}{w_{0}:=\frac{w_{i\quad n}}{{\sqrt{1 + ( \frac{\pi \cdot w_{i\quad n}^{2}}{\lambda \cdot R_{i\quad n}} )}}^{2}}} & {\quad {{2w_{0}} = 14.333}}\end{matrix}$

Launching from Si Membrane side

n:=3.4 L:=7

r_(c):=R_(mems) W_(c):=W₂${q2}:=\lbrack ( {\frac{1}{r_{c}} - \frac{i \cdot \frac{\lambda}{n}}{\pi \cdot w_{c}}} )^{- 1} \rbrack$

q2=−49.869+380.227i $\begin{matrix}{q_{0{im}} = {:={{Im}( \frac{q_{2} - L}{n} )}}} & {\quad {q_{0{re}}:={{Re}( \frac{q_{2} - 1}{n} )}}} & {\quad {q_{0{im}} = 111.831}}\end{matrix}$

q₀:=q_(0re)+i·q_(0im) q_(0re)=−16.276

The radius of curvature and spot entering the Si Membrane are$\begin{matrix}{{R_{i\quad n}:=\frac{1}{{Re}( \frac{1}{q_{0}} )}}\quad} & {\quad {R_{i\quad n}:={- 764.433}}} \\{w_{i\quad n}:=\sqrt{\frac{- \lambda}{\pi} \cdot \frac{1}{{Im}( \frac{1}{q_{0}} )}}} & {{{2w_{i\quad n}} = 15.065}\quad} \\\quad & {{w_{i\quad n} = 7.532}\quad}\end{matrix}$

Therefore, the spot size at the waist in air is $\begin{matrix}{w_{0}:=\frac{w_{i\quad n}}{\sqrt{1 + ( \frac{\pi \cdot w_{i\quad n}^{2}}{\lambda \cdot R_{i\quad n}} )^{2}}}} & {{2w_{0}} = 14.899} \\\quad & {{w_{0} = 7.45}\quad}\end{matrix}$

Once the desired mode size for the tunable filter 18 is determined, thenthe lenses of the filter train are selected and their position isdetermined in step 350.

Specifically, according to the illustrated embodiment, there are twolenses in the filter train: the first lens 14 and the second lens 16.These yield an effective magnification between the mode size at thefiber endface 12 and the tunable filter 18.

Lenses of established curvatures can be used. The positioning of thelenses in train between the fiber endface and the tunable filter isadjusted to yield the preferred mode size at the tunable filter.

Finally, in step 360, the lenses are installed in the filter trainhaving the selected curvatures and locations between the fiber endface12 and the tunable filter 18.

A further extension of above described techniques is to measure mirrors.Mirror astigmatism is manifested in the spectral plot of the filteringfunction by peak splitting in the higher order modes. Measurement of thespectral distance between these sub-peaks is related to the astigmatismin the mirror, or specifically the two radii of curvatures.

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

What is claimed is:
 1. A process for configuring a tunable MOEMS filtertrain, the process comprising: determining a spectral response of aMOEMS tunable filter; determining a spectral separation betweendifferent modes in the spectral response of the tunable filter;determining a mode size of a desired mode of the tunable filter from thespectral separation; and selecting and installing an optical componentin response to the determined mode size into an optical train of thetunable filter to launch light into the tunable filter.
 2. A process asclaimed in claim 1, further comprising determining a mode size of anoptical signal injected into the filter train.
 3. A process as claimedin claim 1, wherein a mode size of an optical signal injected into thefilter train is about 10 micrometers in diameter.
 4. A process asclaimed in claim 1, further comprising injecting an optical signal intothe filter train directly from a single mode optical fiber.
 5. A processas claimed in claim 1, wherein the step of determining the spectralresponse of the tunable filter comprises scanning the tunable filteracross a laser light source.
 6. A process as claimed in claim 1, whereinthe step of determining the spectral response of the tunable filtercomprises scanning the tunable filter across a spectrally narrow line.7. A process as claimed in claim 1, wherein the step of determining thespectral separation between the different modes in the spectral responseof the tunable filter comprises determining the spectral separationbetween a lowest order mode and a next higher order mode within an orderof operation of the tunable filter.
 8. A process as claimed in claim 1,wherein the step of determining the mode size comprises determining themode size of a lowest order mode of the tunable filter.
 9. A process asclaimed in claim 1, wherein the step of selecting and installing theoptical component comprises selecting a lens having beam formingcharacteristics that will yield the determined mode size at the tunablefilter.
 10. A process as claimed in claim 1, wherein the step ofselecting and installing the optical component comprises determining thebeam forming characteristics of the optical component and determining aposition for the optical component that will yield the determined modesize at the tunable filter.
 11. A process as claimed in claim 1, whereinthe step of selecting and installing the optical component comprisesdetermining the beam forming characteristics of the optical componentand installing the optical component to provide a mode field diameter ofbetween 10 and 50 micrometers at the tunable filter.
 12. A tunable MOEMSfilter train, comprising: a MOEMS tunable filter having a spectralresponse, in which a spectral separation between different modes in thespectral response has been measured and a mode size of a desired mode ofthe tunable filter determined; and an optical component that launches aninput signal into the tunable filter, the optical component beingselected and/or placed so that the input signal has the determined modesize at the tunable filter.
 13. A filter train as claimed in claim 12,wherein the optical component comprises a lens.
 14. A filter train asclaimed in claim 12, wherein the determined mode size is between 10 and50 micrometers.